Question

find dy/dx of
xsiny-ycosx=1

Answer 1

use the product rule....

x(siny) - y(cosx) = 1

x(cosy)dy/dx + siny - y(-sinx) - cosx(dy/dx) = 0
dy/dx(xcosy - cosx) = -siny - ysinx
dy/dx = -(siny + ysinx)/(xcosy - cosx)